How to mesh up Ewald sums (I): A theoretical and numerical comparison of various particle mesh routines

TL;DR

This paper compares three FFT-accelerated Ewald sum algorithms (P3M, PME, smooth PME), analyzing their techniques, accuracy, and tuning parameters to identify the most flexible and precise method.

Contribution

It provides a unified view of these algorithms, detailed accuracy assessments, and proposes optimized component combinations, especially favoring P3M.

Findings

Significant accuracy differences among the methods.

Influence of tuning parameters on accuracy.

P3M identified as the most flexible approach.

Abstract

Standard Ewald sums, which calculate e.g. the electrostatic energy or the force in periodically closed systems of charged particles, can be efficiently speeded up by the use of the Fast Fourier Transformation (FFT). In this article we investigate three algorithms for the FFT-accelerated Ewald sum, which attracted a widespread attention, namely, the so-called particle-particle-particle-mesh (P3M), particle mesh Ewald (PME) and smooth PME method. We present a unified view of the underlying techniques and the various ingredients which comprise those routines. Additionally, we offer detailed accuracy measurements, which shed some light on the influence of several tuning parameters and also show that the existing methods -- although similar in spirit -- exhibit remarkable differences in accuracy. We propose combinations of the individual components, mostly relying on the P3M approach, which we regard as most flexible.